### Abstract

We investigate the low-temperature relaxation dynamics toward a nonequilibrium steady state in a tilted asymmetric periodic potential based on the WKB analysis and the numerical diagonalization of the Fokker-Planck operator. Due to the tilting, the Fokker-Planck operator, and thus the Schrödinger operator associated with it, are non-Hermitian. Therefore, we evaluate the decay rate based on the WKB analysis both for real- and complex-valued eigenvalues. In the tilting range where the double-humped barrier exists, the decay rate is shown to obey a law which is a subtle nonequilibrium extension of the so-called Kramers escape rate. The decay rate for the single-humped barrier case is analyzed as well. The large tilting regime where the barriers no longer exist is also investigated.

Original language | English |
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Article number | 031140 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 76 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2007 Sep 28 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*76*(3), [031140]. https://doi.org/10.1103/PhysRevE.76.031140

**Kramers theory in the relaxation dynamics of a tilted asymmetric periodic potential.** / Monnai, Takaaki; Sugita, Ayumu; Nakamura, Katsuhiro.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 76, no. 3, 031140. https://doi.org/10.1103/PhysRevE.76.031140

}

TY - JOUR

T1 - Kramers theory in the relaxation dynamics of a tilted asymmetric periodic potential

AU - Monnai, Takaaki

AU - Sugita, Ayumu

AU - Nakamura, Katsuhiro

PY - 2007/9/28

Y1 - 2007/9/28

N2 - We investigate the low-temperature relaxation dynamics toward a nonequilibrium steady state in a tilted asymmetric periodic potential based on the WKB analysis and the numerical diagonalization of the Fokker-Planck operator. Due to the tilting, the Fokker-Planck operator, and thus the Schrödinger operator associated with it, are non-Hermitian. Therefore, we evaluate the decay rate based on the WKB analysis both for real- and complex-valued eigenvalues. In the tilting range where the double-humped barrier exists, the decay rate is shown to obey a law which is a subtle nonequilibrium extension of the so-called Kramers escape rate. The decay rate for the single-humped barrier case is analyzed as well. The large tilting regime where the barriers no longer exist is also investigated.

AB - We investigate the low-temperature relaxation dynamics toward a nonequilibrium steady state in a tilted asymmetric periodic potential based on the WKB analysis and the numerical diagonalization of the Fokker-Planck operator. Due to the tilting, the Fokker-Planck operator, and thus the Schrödinger operator associated with it, are non-Hermitian. Therefore, we evaluate the decay rate based on the WKB analysis both for real- and complex-valued eigenvalues. In the tilting range where the double-humped barrier exists, the decay rate is shown to obey a law which is a subtle nonequilibrium extension of the so-called Kramers escape rate. The decay rate for the single-humped barrier case is analyzed as well. The large tilting regime where the barriers no longer exist is also investigated.

UR - http://www.scopus.com/inward/record.url?scp=34848860792&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34848860792&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.76.031140

DO - 10.1103/PhysRevE.76.031140

M3 - Article

AN - SCOPUS:34848860792

VL - 76

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 3

M1 - 031140

ER -